Question

You are willing to pay $30,000 now to purchase a perpetuity that will pay you and your heirs $1,200 each year, forever, starting at the end of this year. If your required rate of return does not change, how much would you be willing to pay if this were a 30-year annual payment, ordinary annuity instead of perpetuity?

Answer 1

The required return on perpetuity is calculated below:

Present value = Cash flow Interest rate

30,000 = 1. 200 Interest rate

Interest rate = 1,200 30.000

Interest rate = 0.04

Required return is 4%.

The amount which individual ready to pay for 30 year annuity is calculated below:

1-(1+i) Present value = Cash flow X

Here, i is intererst rate.

n is number of payment.

Present value = 1, 200 x 1 - (1 + 0.04)-30 0.04

Present value = 1,200 x 1 -0.308318668 0.04

Present value = 1, 200 x 17.2920333

Present value = 20, 750.44